Answered: aw- Let Z[/2] = {a +b/2 |a, b e Z} and… | bartleby

Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 28E

See similar textbooks

Related questions

Question

aw-
Let Z[/2] = {a +b/2 |a, b e Z} and let H = {
b
а 2b
: a,b eZ }.
a
Show that Z[ /2] and H are isomorphic as rings.

Expert Solution

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

14. Let be an ideal in a ring with unity . Prove that if then .
19. Find a specific example of two elements and in a ring such that and .
18. Let be a commutative ring with unity, and let be the principal ideal in . Prove that is isomorphic to .
Let R be a commutative ring with characteristic 2. Show that each of the following is true for all x,yR a. (x+y)2=x2+y2 b. (x+y)4=x4+y4
24. If is a commutative ring and is a fixed element of prove that the setis an ideal of . (The set is called the annihilator of in the ring .)
Let R be a commutative ring with unity whose only ideals are {0} and R Prove that R is a field.(Hint: See Exercise 30.)
a. If R is a commutative ring with unity, show that the characteristic of R[ x ] is the same as the characteristic of R. b. State the characteristic of Zn[ x ]. c. State the characteristic of Z[ x ].
If R1 and R2 are subrings of the ring R, prove that R1R2 is a subring of R.
22. Let be a ring with finite number of elements. Show that the characteristic of divides .
15. Prove that if is an ideal in a commutative ring with unity, then is an ideal in .
Let I be an ideal in a ring R with unity. Prove that if I contains an element a that has a multiplicative inverse, then I=R.
14. Let be a ring with unity . Verify that the mapping defined by is a homomorphism.

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Modern Algebra

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elements Of Modern Algebra

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

SEE MORE TEXTBOOKS